Sending a bill with his name on it could automatically alienate Republicans who might otherwise support an overhaul.

Children join a 2010 demonstration calling for changes in immigration… (Chip Somodevilla, Getty…)

WASHINGTON — As President Obama settles on a strategy to overhaul the nation's immigration laws, he faces a quandary that speaks volumes about the bitter nature of politics in a divided capital: The very fact that a plan has Obama's name on it might be enough to kill it.

Obama will relaunch his drive for an immigration overhaul Tuesday in Las Vegas, where heavy turnout by Latino voters in November helped seal his reelection. But some allies in Congress warn that embracing too specific a proposal could mean its death warrant.

Republicans, they say, would feel compelled to oppose a bill identified explicitly with the president. Better, they advise, to announce broad principles and avoid particulars, even if that means violating a campaign pledge to propose legislation. Obama promised to do that in his first campaign, did not deliver, and repeatedly vowed during his reelection campaign to make up for that failure.

The toxic nature of the Obama brand in Republican circles has become a factor that affects White House decisions large and small. Aides still recall with astonishment that when Obama invited members of Congress to the White House to watch the movie "Lincoln" last year, at a screening attended by some of the film's stars, not a single GOP lawmaker attended.

That acute Obama aversion has forced the White House to step carefully as it moves ahead on second-term priorities. On gun control, Obama aides felt he had little to lose by laying out specific recommendations because most Republicans were certain to oppose them.

But on immigration, a bipartisan group of senators is working on a proposal. Legislation from the White House could disrupt that and reduce hopes for major legislation, some lawmakers have warned.

This fight over tactics belies some substantial agreement emerging on the broad areas that must be addressed — the most notable being a growing consensus that any legislation must create a way for the country's estimated 11 million illegal immigrants to obtain legal status. Both Democrats and Republicans also are primed to make changes to the way businesses verify a worker's legal status and to update the criteria for legal immigration.

But in a capital ruled by partisan interests, ambition and egos, agreeing on policy doesn't get the deal done. Democrats remain divided over how aggressively the president should lead, and Republicans — the few who are publicly endorsing the effort — want Obama to stay at a distance.

In a sign of the tension, the bipartisan Senate group, upon hearing of the president's plans for a speech, hustled to finish a statement of principles on immigration to unveil Monday or Tuesday, ahead of Obama's official launch, according to a Senate aide who, like other congressional and White House officials, asked not to be identified to discuss private conversations.

The White House is mindful of the pitfalls ahead, and officials said Obama was moving cautiously.

In his remarks Tuesday, his first major policy speech of his second term, Obama is expected to draw from his May 2011 immigration blueprint and may declare some elements non-negotiable. Among other measures included in the 29-page proposal, Obama emphasized improving border security, expanding the system employers use to verify the legal status of workers and creating a path to citizenship for illegal immigrants.

This leading from the bully pulpit has become Obama's strength in his frequent tussles with Republicans in Congress. Obama has pressured them into raising taxes on the wealthy and giving students a break on their loans, but has had less success in leading by trying to legislate, as Senate Judiciary Committee Chairman Patrick J. Leahy (D-Vt.) encouraged him to do earlier this month.

"If the president does send up specific language, that would make it easier because we'll work from that," Leahy said in an interview on C-SPAN. "[We] may not accept all of it, may add to it. But at least we have something to work from, so that would be very helpful."

Not all Democrats agree. At a meeting with Latino lawmakers at the White House on Friday, Obama heard both pieces of advice, according to people who attended the meeting.

Some lawmakers urged Obama to move quickly, leaving behind the bipartisan effort, while others asked him not to put forward a bill. Obama appeared frustrated, said one congressional aide. "He seemed to say, 'Which is it, you want me to lead but not drop a bill?'" the aide said.

This frustration is familiar to the White House. Obama, who has been described as "leading from behind," has often chosen to take a less engaged role in legislative battles, only to take heat from people in his own party who say he is being too passive.

When Obama does engage directly, his unpopularity among Republicans works against him.